Efficiency estimation for an equilibrium version of the Maxwell refrigerator

Maxwell refrigerator as a device that can transfer heat from a cold to hot temperature reservoir making use of information reservoir was introduced by Mandal et al. [Phys. Rev. Lett. 111, 030602 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.030602]. The model has a two-state demon and a bit stream interacting with two thermal reservoirs simultaneously. We work out a simpler version of the refrigerator where the demon and bit system interact with the reservoirs separately and for a duration long enough to establish equilibrium. The efficiency, η, of the device when working as an engine as well as the coefficient of performance (COP) when working as a refrigerator are calculated. It is shown that the maximum efficiency matches that of a Carnot engine/refrigerator working between the same temperatures, as expected. The COP, when cooling per cycle is a maximum, decreases as 1/T_{h} when T_{h}>T_{c}≫ΔE (k_{B}=1), where T_{h} and T_{c} are the temperatures of the hot and cold reservoirs, respectively, and ΔE is the level spacing of the demon. η, when work per cycle is a maximum, is found to be T_{h}/0.779+T_{h} when T_{c}≪ΔE and T_{h}≫ΔE.